I have a problem solving question and similar to Todd im into the conics section.

1)A section of roller coaster track is in the shape of a parabola. The track spans a horizontal distance of 84 yards and has a maximum height of 32 yards. Six vertical support beams are located at a a distance of 12 yards from each other. Find the sum of the lengths of all six vertical support beams.

1)A section of roller coaster track is in the shape of a parabola. The track spans a horizontal distance of 84 yards and has a maximum height of 32 yards. Six vertical support beams are located at a a distance of 12 yards from each other. Find the sum of the lengths of all six vertical support beams.

1. Define a coordinate system. I suggest the origin to be the midpoint of the horizontal distance.

2. Then the general equation of the parabola is

p(x) = a x^2+32

3. You know the coordinates of V(0, 32) and B(42, 0). Plug in the coordinates of B into the equation of the parabola:

0 = a*(42)² + 32 ==> a = - 8/441

The complete equation is : p(x) = -8/441 * x^2 + 32

4. To use 6 vertical beams you have to divide the horizontal span into 7 equal distances (why?). Make a table and calculate p(-30), p(-18), ... p(30). For symmetry reasons you only have to calculate 3 values.